Physics for Everyone. Molecules

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L,D, Landau A,I,Kitaigorodsky

------Physics for Everyone

MOLECULES Translated from the Russian by Martin Greendlinger, D. Sc. (Math.)

Book 2 ~I

M:r Publishers Moscow

PREFACE TO THE FOURTH RUSSIAN EDITION

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This book has been nalllOd Jlo7ec1I7es. "rany chapters from tbe second half of a previous book, Physics tor Everyone, by Lev Landau and Alexander Kitaigorodsky, have been included without revision. The book is clDvoled mninl v to a studv of the structure of matter dealt with from ~arious aSI~ects. The atom, however, remains. for the time being. Lhe indivisible particle conceived hv DeTIJocritns of ancient Greece. Problems related 10 "he motion of molecules are considerod, of COll[,~O. bocause Ihey are the basis for 0111' modern knO\dedge of thermal motion. AttenLion ha" b.Dl:n g'iv8n, as IYelL 10 problems concC'rning' phas£' tran-

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In ,the years si IICO the preceding Ddi Lion of Physics for lweryolle was rpubli,;]wd, 0111' informaLioli on the strllcLnre of moiecliles and thuir interaction has boen COllsidurably snpplplllellted. \Ianv discoveries Iiave been Ill.ado Lila!' bridgp llip gaps "PtWO~'11 till' problolns dealing w1th tho Illoiecli LII' ,~I I'llclurp of ~II ""Lances and tliei'r proporLies.Tbis IliI' Illdlll'cd Jill' 10 add iI slll>stantial amollnt oj' /le\\ Illall'l'jal A 10/lll OV('I'I!ll(', !llcasuJ'('. " . 1 I 1'1'."' III llJY O]lJIIJOIl, I~ 11(' ilfl[lOll to '" "t'lIlli'II'1 I'll I j' I ' f . ( 1'\ 100 \~ 0 "I'III'ra III Ul'lilatioll 011 lila I eculo..; L1' t . f .' [,I. ,11'(' !llOl'l' ('()JII!'l('.\' tllilll til(' 1l1OIccuies a tox?gen, llitl'ogl'll alld (',ll'huu diu.\'idp. { ]l !'u the presen time th" II ' L.tU IOI'S o! IU'l.~t ('OIIl'Sl'." iJi ]Jhysics have .' no t cons1dered 'L '" . ' , I IIl)Ce""ary to dual \llth 11101'8 compll·· h

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34

Molecules

of thousands of calories per mole. The heat of reaction is often included as a summand in the formula for a reaction. For example, the reaction whereby carbon in the form of graphite burns, Le. unites with oxygen, is written out as follows: C

+

°= 2

CO 2

+ 94 250

cal

This means that when carbon combines with oxygen an energy of !:J4 250 calories is liberated. The sum of the internal energies of a mole of carbon and a mole of oxygen is equal to the internal energy of a mole of carbon dioxide plus 94 250 calories. 'rhus, such formulas have the transparent meaning of algebraic equalities written in terms of the values of the internal energies. With the aid of such equations, one can find the heats of reaction for which direct methods of measurement, as a result of one or another cause, are unsuitable. Here is an example: if carbon (graphite) were to combine with hydro~n, the acetylene would be formed: 2C

+H

2

= C 2H 2

The reaction does not proceed in this manner. Nevertheless, it is possible to find its thermal effect. We write down three known reactions: (1) the oxidation of carbon 2C + 20 2 = 2C0 2 + 188 000 cal (2) the oxidation of hydrogen 1

H 2 + "'2 02 = H 20

+ 68 000

cal

(3) the oxidation of acetylene 5

C2H 2 + T 02 = 2COz + H 2 0

+ 312 000 cal

35

2. Structure of Matter

All these equalities may be regarded as equations for the binding energies of molecules. If so, we may operate on them as on algebraic equalities. Subtracting the first two equalities from the third, we obtain: 2C

+H

2

= C2H 2

-

56 000 cal

Therefore, the reaction we are interested in is accompanied by the consumption of 56 000 calories per mole. Physical and Chemical Molecules

Until investigators had formed a detailed concept of the structure of matter, no such distinction was made. A molecule was simply a molecule, i.e. the smallest representative of a substance. It seemed that nothing more could be said. This is not so, however. The molecules we have just discussed are molecules in both senses of the word. Molecules of carbon dioxide, ammonia and benzene (mentioned above), and the molecules of practically all organic substances (which were not discussed) consist of atoms strongly bonded to one another. These bonds are not ruptured by dissolution, melting or evaporation. The molecule continues to behave as a separate particle or small physical body upon any physical action or change in state. But this is not always true. For most inorganic substances, we can speak of the molecule only in the chemical sense. The finest particles of such well-known inorganic substances as common salt or calcite or soda do not even exist. We do not find separate particles of these substances in crystals (this will be discussed a few pages further on); when they are dissolved, the mOlecules break down into their component atoms. Sugar is an organic substance. Therefore, the sugar dispersed in a cup of sweetened tea is in the form of 3*

M

~~.

molecules. Salt is a difie-eeht matter. We find no molecules of common salt (sodium chloride) in salty water. These "molec~.rles" (we have to use quotation marks) exist in water In the form of atoms (actually, ions-electrically charged atoms-that will be discussed later). The same is true of vapours; and in melts a part oC the molecules live their own independent lives . . When we speak of the forces binding the atoms togetIier In a physical molecule, we call thent' valence forces. Intermolecular forces are not of the valency kind. The general shape of the interaction curve, of the type illustrated in Figure 2.1, is the same for both kinds of forces. The difference lies in the depth of the potential well. For valence forces the well is hundreds of times 'deeper.

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Interaction of Molecules

There can be no doubt of the fact that molecules attract each other. If they stopped doing so for ,an instant all liquids .'and solids would decompose into molecules: Molecules repel each other, and neither can this be doubted, because liquids and solids would otherwise contract with extraordinary ease. . , Forces ine exerted between molecules which resemble in many respects' the forces between atoms spoken of above. The potential energy curve which we have just drawn for atoms gives a true picture of the basic features of molecular interaction. However, there are also essential differences between these interactions. Let us compare, for example, the equilibrium distances between oxygen atoms forming a molecule and oxygen atoms of two neighbouring molecules attracted in solidified oxygen before the equilibrium position. The difference will be very notice~ble: the oxygen atoms forming l\l "

2. Structure of Matter

37

molecule settle down at a' distance of1'.2 'j...,; while the oxygen atoms of. different molecules approach each other to within 2.9 A.. . Analogous results have also b~~n obtained for, other atoms. Atoms of different inolecules settle down farther from each other than atoms"of the same molecule. It is therefore easier to tear m.olecule.s ap'art from each other than atoms from a molecule; moreov;er,. the differehce in energy is much greater than thkt in distance. .wliiJe the energy necessary for breakin¥. the bonds between oxygen atoms forming a molecule 18. a~out 100 kcallmol, the energy neeped to pull oxyge'n molecules asunder is less than 2 kcallmol. .", . , Hence, on a potential energy curve for, molecules, the potential well lies farther ~w:ayfrom the, vertical axis and, furthermore, the well ~s mUCh, shallower. However this does not exhaust. the r diff~ence between the interaction beiween atoms fonning -'a molecule and the int.eraction of' Jllolec.ule's,: .'. .' Cbemistshaves'hownth'at atoms are bound in a molecule with a _fully determined number of other. atoms. H, two hydr,ogen at()1n~ hay~ for~ed a ll?-olecule, no third atom will join them to this end. AI). oxygen atom in water is bound to two. hydrOgen'atoms, a':£1(1' it is impossi,ble ,to bind _~nqther atoJll to, t~~m'. ,.'. ' We do nqtfi,nd' an,ything sim~la~ ~!l ~!1t~r~